A special case of MFGs, called stationary MFGs, is studied in [1]}. The authors present multiple notions of equilibrium and study two-timescale policy gradient methods in this setting, wherein a representative agent updates its policy to best-respond to its (estimated) environment on the fast timescale and updates its estimate for the mean-field flow on the slow timescale. By assuming access to a simulator for obtaining data, convergence to a weak notion of local equilibrium is proved.
